Quantifying 3D Seed Morphology Using Star-Convex Polyhedra

To determine whether the shape of B. napus seeds could be appropriately described by star-convex polygons, the accuracy of reconstruction of ground truth labels for a small subset of 10 3D sub-volumes from the ‘training’ dataset was explored. Accuracy of reconstructed seeds was assessed based on the mean intersection-over-union (IoU) of ground-truth seed labels compared to 3D star-convex polyhedra shape representations of the seed, predicted using the method described by Weigert et al. (2020) in which for each pixel inside a seed the distance to the object boundary is calculated along a fixed set of rays that are approximately evenly distributed on an ellipsoid representative of the seeds within the dataset (see Weigert et al., 2020 eq. 1). The sets of rays used in seed reconstruction were calculated as Fibonacci rays, defined using the method described by Weigert et al. (2020) , which were shown to be more accurate for reconstruction of 3D star-convex polyhedra than equidistant distributed rays and allowed for the potential anisotropy of seed to be taken into account. Reconstruction accuracy was investigated using a varying number of Fibonacci rays (8, 16, 32, 64, 96, and 128), as although Weigert et al. (2020) found a set of at least 64 rays was necessary to achieve accurate reconstruction of shape for cell nuclei, they suggested accurate reconstruction of less anisotropic or densely-packed objects may be possible with a smaller set of rays which would allow for less computational resources to be used in shape prediction.